How can I Extrude Objects According to Their Colors?
There may be a good answer within Blender.  But if you just need to get the job done, you could open your SVG file in Inkscape.  Inkscape has the ability to select objects by the same colors, e.g. select one object with the desired color and choose "Edit --> Select Same --> Fill Color".  In this way you could create several SVG files, each containing only objects of the same color.  You can then import each SVG file separately and give each one a group, so that you can select and edit the group easily.

I did this with a circuit board SVG (a two-dimensional one) I found online with the following results:



The curves can indeed be extruded without converting to meshes, simply modify the "Extrude" value under "Modification" in the "Geometry" section of the curve data tab.  If you want to set all the extrude values at once, join the curves first.  This is a good reason for keeping them as curves for as long as possible, btw.